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REPORT
Trinitas Topology Optimization
Tutorial Document
Henrik Alm Grundström
LIU-IEI-WP--18/00010—SE Horizon 2020
European Union Funding for Research & Innovation
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Trinitas Topology Optimization
Tutorial Document
Table of Contents
1. 2D L-beam With Stress Constraint ... 4 2. 3D Bracket with Stress an AM Overhang Constraints ... 9
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1.
2D L-beam With Stress Constraint
In this example we will minimize the mass of a simple 2D L-Beam subject to a von-Mises stress constraint, see Figure 1.
Figure 1 – L-Beam geometry and boundary conditions.
Start Trinitas and select a name for the database file, name it “Example_1”. Go to the Geometry menu and select Create Point -> Create Points by the Curser. Create points according to the figure below.
Figure 2 – L-Beam points.
Go back by pressing the right mouse button. Go to the Create Line menu and select the straight line icon. Create lines according to the figure below.
5 Figure 3 - L-Beam lines.
Go back to the Geometry menu and select Create Surface create surfaces by selecting all the lines enclosing the surface. The result should look like the figure below.
Figure 4 - L-Beam surfaces.
Go to the Create Volume menu and select Create Volumes with Constant Thickness. Select all the
surfaces to define their thickness. Select Modify Volume and change the thickness to 0.075 m, select
Modify Volume Thicknesses and click on all the surfaces to change their thickness.
Go back to the main menu and select Mesh. Click on Create a Model Mesh from Default Lower-order Elements, a mesh with a single element per volume is created. Click on Modify Model Mesh and use the tools to create a mesh with around 6,000 elements of roughly the same size. The elements can be increased by Increment, Multiplication factor or to a fixed number along a single line or along all lines. The mesh should look something like the figure below. The number of elements in the model can be checked by clicking on Show Model Mesh Element Statistics from the Mesh menu.
6 Figure 5 – L-Beam mesh.
From the main menu, go to Analysis Type > Linear Static Stress Analysis > Topology Optimization -> Exclude Volumes. Click on Exclude Volumes and select the two volumes in the figure below.
Figure 6 - Excluded Volumes
Go back to the main menu and select Boundary Conditions. Select Point Loads and enter -1e5 for the y-component of the force. Select Create a New Point Load and click on the tip of the beam as indicated in the figure below.
7 Figure 7 - L-Beam loadcase
From the Boundary Conditions menu, select Fixed Displacements->Fix a Line-> Fix in both Directions. Select the line at the top of the beam as indicated in the figure below.
Figure 8 - L-Beam boundary conditions
From the main menu, go to Analysis Type -> Linear Static Stress Analysis -> Structural Optimization. Select Minimum Mass in the Select Objective Function menu. Click on Select Constraints and select von Mises Stress. Select Activated in von Mises Stress Constraint, enter 80e6 for the von Mises Stress Limit. The number of stress clusters can be left at 8. Go back to the Structural Optimization menu, select Select Visualized Variable and choose Elemental Porosity. Click on Select Design variables and choose Topology Optimization Variables. Enter 0.5 for the Initial Porosity Value and set the Filter Radius to 0.008. Go back to the Structural Optimization menu, set the Tolerance to 1e-7 and the maximum number of iterations to 500. Click on Start Iterations to start the optimization. The results should be similar to the figure below.
8 Figure 9 - L-Beam results.
In order to get a better view of the results some of the display settings should be changed. From the main menu, go to Draw > Options > Select Visualization Objects and set: Reference Configuration -> None, Current Configuration --> No Mesh and Select Scalar Field --> None. In order to remove the center of gravity symbol, go to Analysis Type -> Analysis Options -> Weight Calculation -> On and set Draw Center of Gravity Symbol -> Not Activated. The results should be displayed as in the figure below.
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3D Bracket with Stress an AM Overhang Constraints
In this example we will minimize the mass of the bracket in Figure 11 subject to stress and AM overhang constraints using three load cases.
Figure 11 – Bracket mesh from HyperMesh.
Start Trinitas and select a name for the database file, name it “Example_2”. Go to Comminication -> Import a new model -> In Abaqus format, click Browse and select the file Bracket_Mesh_BE.inp. Click OK to import the model. This may take several minutes. When the model is displayed, go to Geometry -> Visualization and select Surfaces -> No and Volumes -> No. In order to change the way the model rotates when the middle mouse button is pressed, go to Draw -> Options -> View and change the View Changing Technique to Ball Rotation Algorithm (This is Optional).
Since this is a relatively large imported model some of the graphics is quite slow so some patience is needed, also SAVE OFTEN!
Go to the Mesh menu and select Create a Model Mesh from default Lower-Order Elements. Since the model is imported as a mesh file all information about the original CAD geometry is lost and each element is treated as a separate volume in Trinitas. In order to work with the model it is therefore necessary to create groups of elements. Three element groups already exist in the model, see Figure 12, these were created as element sets in HyperMesh. In order to view and create groups go to Geometry -> Create Group. The groups that already exist in the model are for the design space (included), the functional areas (excluded) and the boundary extension. The boundary extension is used to represent void outside of the design space in order to avoid boundary effects.
10 Figure 12 – Bracket groups defined in HyperMesh.
In order to apply the boundary conditions a few more groups have to be created. In the Create Group menu, select of Lines, Surfaces or Volumes from Points. In order to use this function extra nodes were
created in HyperMesh at the centres of the cylindrical surfaces where the boundary conditions are applied. Select Pick Points defining a Centreline and a Radius of a Cylinder and select the point according to the figure below.
11 Then select Create Group of -> Surfaces on a Cylinder. The first surface group is now created, repeat this step until you have defined all the groups in the figure below.
Figure 14 – Groups for boundary conditions.
In order to simplify the application of the boundary conditions the groups themselves can be grouped. In order to do this, go to Geometry -> Modify Group -> Join Groups. Join the groups so that the four vertical holes are in one group and the two horizontal groups are in one. Select the groups you want to join and then click the right mouse button to confirm the selection.
The four vertical holes will be fixed in all directions. In order to achieve this, from the main menu go to Boundary Conditions -> Fixed Displacements -> Fix a Surface -> Fix in all Directions and select the inner surface of one of the vertical holes. The program will ask if you want to apply this boundary condition to all the members of the group, select OK. The boundary conditions will be created, this will
take a while due to the graphical representation. In order to speed up this process the boundary
condition symbols can be hidden by selecting Visualization -> No.
It´s now time to define the load cases, in order to do this go to Boundary Conditions -> Surface Loads. For the y-direction enter -50e6*cos(0.583*t+0.393) and for the z-direction enter 50e6*sin(0.583*t+0.393). Click Create a New Surface Load and select the inner surface of one of the horizontal holes. This defines a surface load of 50 MPa where the direction varies as a function of the time (t), see figure below. Go to Time Dependencies -> Select Current Intensity Function -> Constant then select Connect current intensity function and select the inner surface of one of the holes where the load was applied. The intensity function is used to vary the magnitude of the load with time, but in this case we want the magnitude to be constant. We also need to define the time steps used in the
12 optimization, to do this go to Analysis Type -> Linear Static Stress Analysis -> Time Domain Options. Enter 0 in First Time for Analysis, 0.5 in Time Step Size and 1 in Last Time for Analysis.
Figure 15 – Bracket load cases.
Now we want to define the functional and boundary extension parts of the body, in order to do this, go to Analysis Type -> Linear Static Stress Analysis -> Topology Optimization -> Exclude Volumes, in the menu, select Excluded Volumes and select one of the elements on the inner surface of one of the two horizontal holes. Now select Exclude Volumes -> Boundary Extension and select one of the elements in the Boundary Extension group. Once this is done the model has to be remeshed, go to the Mesh menu and select Create a Model Mesh from Default Lower-Order Elements.
It is now time to define the optimization problem, go to Analysis Type -> Linear Static Stress Analysis -> Structural Optimization. Select Minimum Mass as the objective function. Define a von-Mises stress constraint of 250e6 N/mm^2 with 8 stress clusters. In Select Design Variables -> Topology Optimization Variables, set the initial porosity value to 0.5, P-Norm Exponent to 12 and Filter Radius to 0.003. In the Additive Manufacturing Filter menu, set Additive Manufacturing Filter -> Activated, Max. Overhang Angle to 45 and set the Build Direction to X=0, Y=0, Z=1. Go back to the Structural Optimization menu and set Select Visualized Variable to Elemental Porosity, Select Redrawing Frequency to Never, Set Tolerance to 1e-6, Maximum iterations to 250.
Since this is a large model it is recommended to run it in the background, go to the main menu and save the model. Then select Stop -> Start Background Job -> Structural Optimization. A text file called OPT_HISTORY.txt is created in the same folder as the Trinitas.exe file. The progress of the optimization can be followed in this file. Once the optimization is complete Trinitas will close automatically. This will take approximately 60 minutes in this particular case.
NOTE: If you want to abort the optimization create a text-file called Message.txt in the Trinitas.exe folder and enter ABORT, then save and update the file until the text changes to Message Read!
Optimization is Aborting… Wait for the program to close and then reopen it to view the current results.
When the optimization is done, reopen Trinitas. Go to Analysis Type > Linear Static Stress Analysis -> Structural Optimization --> Examine Results --> Create STL File. Select a file name and click OK, this will create a stl-file of the iso-surface with a density value of 0.5. The results should look like the figure below. Close the program without saving!
13 Figure 16 – Bracket Topology.
